Filtering for a Continuous Multi-Resources cumulative Constraint with Resource Consumption and Production

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Within the framework of continuous and multi-resources cumulative constraints, a task T expresses a piecewise linear resource function and is represented by a sequence of p contiguous trapezoid sub-tasks with variable durations and heights. In this context, this paper provides an algorithm in O(p) for filtering the resource assignment and the temporal attributes of such a task, according to a trapezoid of a minimum cumulated resource profile, in order to avoid an overflow of the resource capacity.